Predator-prey harvesting model with fatal disease in prey

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4 Citations (Scopus)

Abstract

A theoretical eco-epidemiological model of a prey-predator interaction system with disease in prey species is studied. Predator consumes both susceptible and infected prey population, but predator also feeds preferentially on many numerous species, which are over represented in the predator's diet. Equilibrium points of the system are determined, and the dynamic behaviour of the system is investigated around equilibrium points. Death rate of predator species is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighbourhood of the coexisting equilibria. Numerical simulations are carried out to support the analytical results.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
DOIs
Publication statusAccepted/In press - 2015

Fingerprint

Predator-prey
Hopf bifurcation
Bifurcation (mathematics)
Harvesting
Predator
Prey
Nutrition
Computer simulation
Equilibrium Point
Prey-predator
Epidemiological Model
Model
Hopf Bifurcation
Dynamic Behavior
Bifurcation
Numerical Simulation
Interaction

Keywords

  • Bifurcation
  • Optimal harvesting
  • Predator
  • Prey
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

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title = "Predator-prey harvesting model with fatal disease in prey",
abstract = "A theoretical eco-epidemiological model of a prey-predator interaction system with disease in prey species is studied. Predator consumes both susceptible and infected prey population, but predator also feeds preferentially on many numerous species, which are over represented in the predator's diet. Equilibrium points of the system are determined, and the dynamic behaviour of the system is investigated around equilibrium points. Death rate of predator species is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighbourhood of the coexisting equilibria. Numerical simulations are carried out to support the analytical results.",
keywords = "Bifurcation, Optimal harvesting, Predator, Prey, Stability",
author = "Khan, {Qamar J A} and Mohamed Al-Lawatia and Al-Kharousi, {Fatma A.}",
year = "2015",
doi = "10.1002/mma.3718",
language = "English",
journal = "Mathematical Methods in the Applied Sciences",
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T1 - Predator-prey harvesting model with fatal disease in prey

AU - Khan, Qamar J A

AU - Al-Lawatia, Mohamed

AU - Al-Kharousi, Fatma A.

PY - 2015

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N2 - A theoretical eco-epidemiological model of a prey-predator interaction system with disease in prey species is studied. Predator consumes both susceptible and infected prey population, but predator also feeds preferentially on many numerous species, which are over represented in the predator's diet. Equilibrium points of the system are determined, and the dynamic behaviour of the system is investigated around equilibrium points. Death rate of predator species is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighbourhood of the coexisting equilibria. Numerical simulations are carried out to support the analytical results.

AB - A theoretical eco-epidemiological model of a prey-predator interaction system with disease in prey species is studied. Predator consumes both susceptible and infected prey population, but predator also feeds preferentially on many numerous species, which are over represented in the predator's diet. Equilibrium points of the system are determined, and the dynamic behaviour of the system is investigated around equilibrium points. Death rate of predator species is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighbourhood of the coexisting equilibria. Numerical simulations are carried out to support the analytical results.

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KW - Optimal harvesting

KW - Predator

KW - Prey

KW - Stability

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